Variable-cell method for stress-controlled jamming of athermal, frictionless grains

Abstract

A new method is introduced to simulate jamming of polyhedral grains under controlled stress that incorporates global degrees of freedom through the metric tensor of a periodic cell containing grains. Jamming under hydrostatic/isotropic stress and athermal conditions leads to a precise definition of the ideal jamming point at zero shear stress. The structures of tetrahedra jammed hydrostatically exhibit less translational order and lower jamming-point density than previously described 'maximally random jammed' hard tetrahedra. Under the same conditions, cubes jam with negligible nematic order. Grains with octahedral symmetry jam in the large-system limit with an abundance of face-face contacts in the absence of nematic order. For sufficiently large faceface contact number, percolating clusters form that span the entire simulation box. The response of hydrostatically jammed tetrahedra and cubes to shear-stress perturbation is also demonstrated with the variable-cell method.

Cluster and constraint analysis in tetrahedron packings

“…In addition, the deformation of the packing boundary is also introduced to check the effect of boundary conditions. The results of cluster distributions and cluster amounts in the deforming boundary case turn out to be consistent with that in the cubic boundary case (without boundary deformation), which supports the conclusion of Smith et al [18], In this sec tion, the properties of local structures in tetrahedron packings are investigated, and the amount of particles participating in forming dimers is suggested as an order metric. A constraint analysis is carried out to study the stability of tetrahedron packings.…”

“…The reason for these disparities is that we apply a more strict F2F contact restriction in the constraint-counting procedure, in which the angle between the contacted faces is smaller than 0.1°. Interestingly, the density of this packing is 0.6337, which is much smaller than the MRJ packing density 0.763 ± 0.005 obtained by Jiao et al [19], but close to the aforementioned jamming threshold density of athermal, soft tetrahedra (<p = 0.62 ~ 0.64, [16][17][18]). Notably, the packing density of the MRI packing of hard tetrahedra is slightly less than that of the MRJ packing of spheres (tp 0.64).…”

“…The expansion speed of the packing space and the magnitudes of translational and rotational movements are controlled to produce samples with different packing densities and order levels. Smith et al [18] investigated the effect of boundary conditions and found that variable boundaries have negligible effects on the jamming of tetrahedra. Consequently, cubic boundary conditions are mostly used in this work.…”

“…There are three strong peaks in the RDF curve of the jammed packing in Ref. [19], while only two peaks with lower values appear in the curves of the new MRJ packing and the soft jammed packings [16,18]. The first three peaks in the RDF may correspond to three [19], and soft jammed packings in Refs.…”

“…Smith et al [16][17][18] obtained the jamming threshold density of athermal, soft tetrahedra (<p = 0.62 ~ 0.64), while Jiao et al [19] proposed that the density of the maximally random jammed (MRJ) packing of hard tetrahedra is 0.763 ± 0.005. Smith et al [18] explained this discrepancy from a kinetic sense, as thermalization enables packing systems to overcome barriers in the athermally jammed structures with low packing densities. A jammed and disordered glass phase of tetrahedra (<p = 0.7858) was reported by Haji-Akbari et al [8].…”